# Probability

In: Other Topics

Submitted By ankurbarot
Words 5830
Pages 24
Prof. Dr. Somesh Kumar
Department of Mathematics
Indian Institute of Technology, Kharagpur
Module No. #01
Lecture No. #07
Random Variables

So, far we were discussing the laws of probability so, in the laws of the probability we have a random experiment, as a consequence of that we have a sample space, we consider a subset of the, we consider a class of subsets of the sample space which we call our event space or the events and then we define a probability function on that.
Now, we consider various types of problems for example, calculating the probability of occurrence of a certain number in throwing of a die, probability of occurrence of certain card in a drain probability of various kinds of events.
However, in most of the practical situations we may not be interested in the full physical description of the sample space or the events; rather we may be interested in certain numerical characteristic of the event, consider suppose I have ten instruments and they are operating for a certain amount of time, now after amount after working for a certain amount of time, we may like to know that, how many of them are actually working in a proper way and how many of them are not working properly.
Now, if there are ten instruments, it may happen that seven of them are working properly and three of them are not working properly, at this stage we may not be interested in knowing the positions, suppose we are saying one instrument, two instruments and so, on tenth instrument, 1 2 up to 10, we are not very particular whether instrument number one has failed or two has failed or ten has failed; that means, which three of them have failed, may not be of interest, rather we are interested in the total number of the instruments, which have failed and total number which have which are working.

(Refer Slide Time: 02:04)

Ah you look at say a game of...

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